A point on the rim of a rotating flywheel experiences both tangential acceleration and radial acceleration.
Tangential Acceleration: The tangential acceleration refers to the change in the linear velocity of the point on the rim. As the flywheel rotates, the point on its rim moves in a circular path. The tangential acceleration represents the rate of change of linear velocity along this circular path. The magnitude of the tangential acceleration can be calculated using the formula:
Tangential acceleration (a_t) = r * α
where r is the distance from the center of rotation to the point on the rim, and α is the angular acceleration.
In the given scenario, it is mentioned that the flywheel rotates with a constant angular velocity. Since angular velocity is constant, the angular acceleration (α) is zero. Therefore, the tangential acceleration (a_t) at any point on the rim is also zero. This means that the magnitude and direction of the tangential acceleration are constant (zero) throughout the rotation.
Radial Acceleration: The radial acceleration refers to the acceleration towards the center of the circular path. It is caused by the change in direction of the velocity vector as the point on the rim moves along the curved path. The magnitude of the radial acceleration can be calculated using the formula:
Radial acceleration (a_r) = r * ω^2
where r is the distance from the center of rotation to the point on the rim, and ω is the angular velocity.
In the given scenario, it is mentioned that the angular velocity of the flywheel is constant. Therefore, the magnitude of the radial acceleration (a_r) is constant throughout the rotation. However, the direction of the radial acceleration changes continuously because it always points towards the center of the circular path.
In summary, a point on the rim of a rotating flywheel has both tangential acceleration and radial acceleration. The tangential acceleration is zero when the angular velocity is constant, while the radial acceleration has a constant magnitude but changing direction (always pointing towards the center of the circular path).